Method for detecting transmission symbols in multiple antenna system

ABSTRACT

The present invention relates to a transmission symbol detection method in a multiple antenna system. In the present invention, when a channel matrix is estimated through channel estimation, a receiving side calculates a Q matrix and an R matrix through QR decomposition that is more simplified than a typical QR decomposition from an augmented channel matrix that includes the estimated channel matrix. In addition, the receiving side detects symbols having the minimum Euclidean metric by using the two matrixes, as transmission symbols.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to and the benefit of Korean PatentApplication No. 10-2007-0128430 filed in the Korean IntellectualProperty Office on Dec. 11, 2007, the entire contents of which areincorporated herein by reference.

BACKGROUND OF THE INVENTION

(a) Field of the Invention

The present invention relates to a transmission symbol detection methodin a multiple antenna system. Particularly, it relates to a transmissionsymbol detection method in a multiple antenna system including aplurality of transmitting antennas.

(b) Description of the Related Art

For a mobile communication system such as IEEE 802.16e that uses fourtransmitting antennas, three usable space-time codes are defined fortransmission. The three space-time codes are denoted as three matrixesA, B, and C, and each has a different symbol transmission rate and adifferent diversity gain. Particularly, the space-time code B has goodtradeoff performance in symbol transmission rate and diversity gain, andcan be represented as shown in Equation 1.

$\begin{matrix}{B = \begin{bmatrix}s_{1} & {- s_{2}^{*}} & s_{5} & {- s_{7}^{*}} \\s_{2} & s_{1}^{*} & \underset{6}{s} & {- s_{8}^{*}} \\s_{3} & {- s_{4}^{*}} & s_{7} & s_{5}^{*} \\s_{4} & s_{3}^{*} & s_{8} & s_{6}^{*}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack\end{matrix}$

Here, the vertical axis denotes an antenna, and four symbols aresimultaneously transmitted from four antennas. The horizontal axisdenotes time or carrier frequency.

When symbols are transmitted by using the above-given space-time codes,the symbols are simultaneously received at a receiving side, andtherefore the entire performance of the system greatly depends on adetection method of the receiving side. Among many conventionaldetection methods, the maximum likelihood (ML) detection method resultsin the best performance.

However, the ML detection method is very complex. Particularly, the MLdetection method has a drawback of being incapable of real-timedetection since the system complexity increases as the size of theconstellation (e.g., 16-QAM or 64-QAM) increases.

Accordingly, in order to reduce system complexity while providing thebest performance (i.e., ML performance), a sphere decoding method hasbeen proposed. The sphere decoding method detects constellation pointsthat are close to a received signal, and therefore the system complexityis lower than a simple ML detection method. However, the sphere decodingmethod has a problem of complexity, and, in the worst case, the spheredecoding method causes exponential functional complexity so that therestill exists a problem in application of the sphere decoding method toan actual system.

Therefore, in order to fundamentally decrease the system complexity,methods that can provide suboptimal performance need to be considered,and the methods include zero-forcing (ZF), minimum mean squared error(MMSE), ZF with successive interference cancellation (ZF-SIC), and MMSEwith SIC. However, those methods provide suboptimal performance that ismore deteriorated than the performance of the ML detection method.

The above information disclosed in this Background section is only forenhancement of understanding of the background of the invention andtherefore it may contain information that does not form the prior artthat is already known in this country to a person of ordinary skill inthe art.

SUMMARY OF THE INVENTION

The present invention has been made in an effort to provide atransmission symbol detection method having advantages of reducingcomplexity and improving performance.

An exemplary transmission symbol detection method in a multiple antennasystem that includes a plurality of transmission antennas according toone embodiment of the present invention includes: estimating a firstmatrix that is a channel matrix including a plurality of channel gainsrespectively corresponding to the plurality of transmission antennas byusing a received signal; calculating a second matrix that is anupper-triangle matrix and a third matrix that is a unitary matrix fromthe first matrix; and detecting a plurality of transmission symbols byperforming successive interference cancellation (SIC) based on thesecond and third matrixes. The second matrix includes a first componentthat corresponds to a first channel gain of the first matrix and asecond component that is calculated based on the first channel gain anda second channel gain that is different from the first channel gain asdiagonal components. The second matrix further includes a plurality ofcomponents using the first channel gain and a plurality of channel gainsthat are different from the first channel gain.

According to the exemplary embodiment of the present invention, atransmission symbol detection method that can reduce complexity in areceiving side and improve performance can be realized.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a system according to an exemplaryembodiment of the present invention.

FIG. 2 is a flowchart of a transmission symbol detection method at areceiving side according to the exemplary embodiment of the presentinvention.

FIG. 3 shows a successive interference cancellation (SIC) detectionmethod in a case of employing a typical BPSK algorithm.

FIG. 4 shows an SIC detection method in case of using a binary phaseshift keying (BPSK) algorithm according to an exemplary embodiment ofthe present invention.

FIG. 5 shows a determination area for a feedback detection valuedetermination when the SIC detection method is applied to 16-QAMaccording to the exemplary embodiment of the present invention.

FIG. 6 compares a bit error rate (BER) of the transmission detectionmethod according to the exemplary embodiment of the present inventionand a typical ZF-SIC and MMSE-SIC method.

DETAILED DESCRIPTION OF THE EMBODIMENTS

In the following detailed description, only certain exemplaryembodiments of the present invention have been shown and described,simply by way of illustration. As those skilled in the art wouldrealize, the described embodiments may be modified in various differentways, all without departing from the spirit or scope of the presentinvention. Accordingly, the drawings and description are to be regardedas illustrative in nature and not restrictive. Like reference numeralsdesignate like elements throughout the specification.

Throughout this specification and the claims which follow, unlessexplicitly described to the contrary, the word “comprising” andvariations such as “comprises” will be understood to imply the inclusionof stated elements but not the exclusion of any other elements.

A transmission symbol detection method in a multiple antenna system thatincludes a plurality of transmitting antennas according to an exemplaryembodiment of the present invention will be described in detail withreference to the drawings.

When four transmitting antennas are used, it is assumed that thetime-space code B uses the 4×4 matrix as given in Equation 1, and thethird and fourth columns of the 4×4 matrix transmit transmission symbolsthat are different from transmission symbols transmitted at the firstand second columns. Since a receiving terminal receive space-time codesat different time slots or different frequencies, it is assumed that thespace-time code includes the first and second columns as shown inEquation 2 for better comprehension and ease of description.

$\begin{matrix}{X = \begin{bmatrix}x_{1} & {- x_{2}^{*}} \\x_{2} & x_{1}^{*} \\x_{3} & {- x_{4}^{*}} \\x_{4} & x_{3}^{*}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

With such an assumption, a transmission symbol detection methodaccording to an exemplary embodiment of the present invention will bedescribed in further detail.

FIG. 1 is a schematic diagram of a system according to the exemplaryembodiment of the present invention.

It is assumed in FIG. 1 that n_(R) receiving antennas exist in thereceiving terminal (i.e., detector). Under this assumption, signalsreceived at the first and second time-slots in a receiving side aregiven as Equation 3.

r ₁ ^(j) =h _(j,1) x ₁ +h _(j,2) x ₂ +h _(j,3) x ₃ +h _(j,4) x ₄ +n ₁^(j)

r ₂ ^(j) =−h _(j,1) x* ₂ +h _(j,2) x* ₁ −h _(j,3) x* ₄ h _(j,4) x* ₃ n ₂^(j)   [Equation 3]

Where h_(j,i) denotes a channel gain between the i-th transmittingantenna and the j-th receiving antenna, and n_(t) ^(j) denotes a whitenoise at the t-th time slot of the j-th receiving antenna.

A received signal r received at the receiving side can be represented asa matrix as shown in Equation 4.

                                                             [Equation  4]     r = Hs + n     r = [[r₁¹], [r₁¹], [r₂¹], [r₂¹], …  , [r₁^(n_(r))], [r₁^(n_(r))], [r₂^(n_(r))], [r₂^(n_(r))]]^(T)$H = \begin{bmatrix}{\left\lbrack h_{1,1} \right\rbrack} & {- {\left\lbrack h_{1,1} \right\rbrack}} & {\left\lbrack h_{1,2} \right\rbrack} & {- {\left\lbrack h_{1,2} \right\rbrack}} & {\left\lbrack h_{1,3} \right\rbrack} & {- {\left\lbrack h_{1,3} \right\rbrack}} & {\left\lbrack h_{1,4} \right\rbrack} & {- {\left\lbrack h_{1,4} \right\rbrack}} \\{\left\lbrack h_{1,1} \right\rbrack} & {\left\lbrack h_{1,1} \right\rbrack} & {\left\lbrack h_{1,2} \right\rbrack} & {\left\lbrack h_{1,2} \right\rbrack} & {\left\lbrack h_{1,3} \right\rbrack} & {\left\lbrack h_{1,3} \right\rbrack} & {\left\lbrack h_{1,4} \right\rbrack} & {\left\lbrack h_{1,4} \right\rbrack} \\{\left\lbrack h_{1,2} \right\rbrack} & {\left\lbrack h_{1,2} \right\rbrack} & {- {\left\lbrack h_{1,1} \right\rbrack}} & {- {\left\lbrack h_{1,1} \right\rbrack}} & {\left\lbrack h_{1,4} \right\rbrack} & {\left\lbrack h_{1,4} \right\rbrack} & {- {\left\lbrack h_{1,3} \right\rbrack}} & {- {\left\lbrack h_{1,3} \right\rbrack}} \\{\left\lbrack h_{1,2} \right\rbrack} & {- {\left\lbrack h_{1,2} \right\rbrack}} & {- {\left\lbrack h_{1,1} \right\rbrack}} & {\left\lbrack h_{1,1} \right\rbrack} & {\left\lbrack h_{1,4} \right\rbrack} & {- {\left\lbrack h_{1,4} \right\rbrack}} & {- {\left\lbrack h_{1,3} \right\rbrack}} & {\left\lbrack h_{1,3} \right\rbrack} \\\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\{\left\lbrack h_{n_{r},1} \right\rbrack} & {- {\left\lbrack h_{n_{r},1} \right\rbrack}} & {\left\lbrack h_{n_{r},2} \right\rbrack} & {- {\left\lbrack h_{n_{r},2} \right\rbrack}} & {\left\lbrack h_{n_{r},3} \right\rbrack} & {- {\left\lbrack h_{n_{r},3} \right\rbrack}} & {\left\lbrack h_{n_{r},4} \right\rbrack} & {- {\left\lbrack h_{n_{r},4} \right\rbrack}} \\{\left\lbrack h_{n_{r},1} \right\rbrack} & {\left\lbrack h_{n_{r},1} \right\rbrack} & {\left\lbrack h_{n_{r},2} \right\rbrack} & {\left\lbrack h_{1,2} \right\rbrack} & {\left\lbrack h_{n_{r},3} \right\rbrack} & {\left\lbrack h_{n_{r},3} \right\rbrack} & {\left\lbrack h_{n_{r},4} \right\rbrack} & {\left\lbrack h_{n_{r},4} \right\rbrack} \\{\left\lbrack h_{n_{r},2} \right\rbrack} & {\left\lbrack h_{n_{r},2} \right\rbrack} & {- {\left\lbrack h_{n_{r},1} \right\rbrack}} & {- {\left\lbrack h_{1,1} \right\rbrack}} & {\left\lbrack h_{n_{r},4} \right\rbrack} & {\left\lbrack h_{n_{r},4} \right\rbrack} & {- {\left\lbrack h_{n_{r},3} \right\rbrack}} & {- {\left\lbrack h_{n_{r},3} \right\rbrack}} \\{\left\lbrack h_{n_{r},2} \right\rbrack} & {- {\left\lbrack h_{n_{r},2} \right\rbrack}} & {- {\left\lbrack h_{n_{r},1} \right\rbrack}} & {\left\lbrack h_{1,1} \right\rbrack} & {\left\lbrack h_{n_{r},4} \right\rbrack} & {- {\left\lbrack h_{n_{r},4} \right\rbrack}} & {- {\left\lbrack h_{n_{r},3} \right\rbrack}} & {\left\lbrack h_{n_{r},3} \right\rbrack}\end{bmatrix}$ $\begin{matrix}{\mspace{79mu} {s:=\left\lbrack {{\left\lbrack x_{1} \right\rbrack},{\left\lbrack x_{1} \right\rbrack},{\left\lbrack x_{2} \right\rbrack},{\left\lbrack x_{2} \right\rbrack},{\left\lbrack x_{3} \right\rbrack},{\left\lbrack x_{3} \right\rbrack},{\left\lbrack x_{4} \right\rbrack},{\left\lbrack x_{4} \right\rbrack}} \right\rbrack^{T}}} \\{\text{=:}\left\lbrack {s_{1},s_{2},s_{3},s_{4},s_{5},s_{6},s_{7},s_{8}} \right\rbrack}^{T}\end{matrix}$     n = [[n₁¹], [n₁¹], [n₂¹], [n₂¹], …  , [n₁^(n,)], [n₁^(n,)], [n₂^(n,)], [n₂^(n,)]]^(T)

Here, r denotes a received signal, H denotes a channel matrix, and ndenotes noise. In addition,

[•] denotes a real part and

[•] denotes an imaginary part. That is, each transmission symbolincludes a real part and an imaginary part.

A transmission symbol detection method for the above-stated system modelwill be described in further detail with reference to equations.

According to the exemplary embodiment of the present invention, asub-optimal detection method based on minimum mean squared error(MMSE)-zero-forcing successive interference cancellation (ZF-SIC) isused for transmission symbol detection.

To use the suboptimal detection method, an augmented channel matrix{tilde over (H)} shown in Equation 5 is used. In addition, the augmentedchannel matrix {tilde over (H)} is QR-decomposed as shown in Equation 5so that matrixes {tilde over (Q)} and {tilde over (R)} are generated.

$\begin{matrix}{\overset{\sim}{H}:={\begin{bmatrix}H \\{\frac{1}{\sqrt{\gamma}}I_{8 \times 8}}\end{bmatrix} = {{\overset{\sim}{Q}\overset{\sim}{R}} = {\begin{bmatrix}{\overset{\sim}{Q}}_{1} \\{\overset{\sim}{Q}}_{2}\end{bmatrix}\overset{\sim}{R}}}}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

Here, {tilde over (Q)} denotes a (4n_(R)+8)×8 unitary matrix, and {tildeover (R)} is a (8×8) upper-triangle matrix. In addition, {tilde over(Q)}₁ is a (4n_(R)×8) sub-matrix of {tilde over (Q)}, and {tilde over(Q)}₂ is a (8×8) sub-matrix of {tilde over (Q)}.

Conventionally, the matrixes {tilde over (Q)}₁ and {tilde over (R)} arecalculated by using a numerical method, and the Gram-Schmidt methodwhich is the representative numerical calculation method is used.However, such a numerical calculation method gives good theoreticalperformance, but it is not appropriate for actual use because an actualoutput matrix {tilde over (Q)}₁ and an expected unitary matrix maydiffer from each other. Therefore, a modified Gram-Schmidt scheme isactually applied to the system, but it has a problem of increasingcomplexity more than the existing Gram-Schmidt scheme. Particularly, themodified Gram-Schmidt scheme should be performed twice to achievesatisfactory performance when a given matrix is ill-conditioned, and,accordingly, complexity is doubled.

Therefore, for solving the numerical calculation method, a method formathematically calculating the QR decomposition and calculating matrixes{tilde over (Q)}₁ and {tilde over (R)} by using a closed-form formulaaccording to the exemplary embodiment of the present invention will nowbe described.

First, assume that {tilde over (h)}_(i), i=1, 2, . . . , 8, and denotesthe i-th column of the matrix {tilde over (H)}. Then the augmentedchannel matrix {tilde over (H)} can be represented as Equation 6.

{tilde over (H)}=[{tilde over (h)} ₁ , {tilde over (h)} ₂ , {tilde over(h)} ₃ , {tilde over (h)} ₄ , {tilde over (h)} ₅ , {tilde over (h)} ₆ ,{tilde over (h)} ₇ , {tilde over (h)} ₈]  [Equation 6]

In addition, the matrix {tilde over (R)} that is QR-decomposed from theaugmented channel matrix {tilde over (H)} can be represented by using aclosed form formula as shown in Equation 7.

$\begin{matrix}{\overset{\sim}{R} = \begin{bmatrix}{\overset{\sim}{R}}_{1,1} & 0 & 0 & 0 & {\overset{\sim}{R}}_{1,5} & {\overset{\sim}{R}}_{1,6} & {\overset{\sim}{R}}_{1,7} & {\overset{\sim}{R}}_{1,8} \\0 & {\overset{\sim}{R}}_{2,2} & 0 & 0 & {\overset{\sim}{R}}_{2,5} & {\overset{\sim}{R}}_{2,6} & {\overset{\sim}{R}}_{2,7} & {\overset{\sim}{R}}_{2,8} \\0 & 0 & {\overset{\sim}{R}}_{3,3} & 0 & {\overset{\sim}{R}}_{3,5} & {\overset{\sim}{R}}_{3,6} & {\overset{\sim}{R}}_{3,7} & {\overset{\sim}{R}}_{3,8} \\0 & 0 & 0 & {\overset{\sim}{R}}_{4,4} & {\overset{\sim}{R}}_{4,5} & {\overset{\sim}{R}}_{4,6} & {\overset{\sim}{R}}_{4,7} & {\overset{\sim}{R}}_{4,8} \\0 & 0 & 0 & 0 & {\overset{\sim}{R}}_{5,5} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {\overset{\sim}{R}}_{6,6} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {\overset{\sim}{R}}_{7,7} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & {\overset{\sim}{R}}_{8,8}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack\end{matrix}$

Here, each element of the matrix {tilde over (R)} can be represented asshown in Equation 8.

$\begin{matrix}{{{{\overset{\sim}{R}}_{1,1} = {{\overset{\sim}{h}}_{1}}};{{\overset{\sim}{R}}_{1,2} = {{\frac{1}{{\overset{\sim}{R}}_{1,1}}{\overset{\sim}{h}}_{1}^{T}{\overset{\sim}{h}}_{2}} = 0}};{{\overset{\sim}{R}}_{1,3} = {{\frac{1}{{\overset{\sim}{R}}_{1,1}}{\overset{\sim}{h}}_{1}^{T}{\overset{\sim}{h}}_{3}} = 0}};{{\overset{\sim}{R}}_{1,4} = {{\frac{1}{{\overset{\sim}{R}}_{1,1}}{\overset{\sim}{h}}_{1}^{T}{\overset{\sim}{h}}_{4}} = 0}}}{{{\overset{\sim}{R}}_{1,5} = {\frac{1}{{\overset{\sim}{R}}_{1,1}}{\overset{\sim}{h}}_{1}^{T}{\overset{\sim}{h}}_{5}}};{{\overset{\sim}{R}}_{1,6} = {\frac{1}{{\overset{\sim}{R}}_{1,1}}{\overset{\sim}{h}}_{1}^{T}{\overset{\sim}{h}}_{6}}};{{\overset{\sim}{R}}_{1,7} = {\frac{1}{{\overset{\sim}{R}}_{1,1}}{\overset{\sim}{h}}_{1}^{T}{\overset{\sim}{h}}_{7}}};{{\overset{\sim}{R}}_{1,8} = {\frac{1}{{\overset{\sim}{R}}_{1,1}}{\overset{\sim}{h}}_{1}^{T}{\overset{\sim}{h}}_{8}}}}{{{\overset{\sim}{R}}_{2,2} = {{{\overset{\sim}{h}}_{2}} = {\overset{\sim}{R}}_{1,1}}};{{\overset{\sim}{R}}_{2,3} = {{\frac{1}{{\overset{\sim}{R}}_{2,2}}{\overset{\sim}{h}}_{2}^{T}{\overset{\sim}{h}}_{3}} = 0}};{{\overset{\sim}{R}}_{2,4} = {{\frac{1}{{\overset{\sim}{R}}_{2,2}}{\overset{\sim}{h}}_{2}^{T}{\overset{\sim}{h}}_{4}} = 0}};{{\overset{\sim}{R}}_{2,5} = {{\frac{1}{{\overset{\sim}{R}}_{2,2}}{\overset{\sim}{h}}_{2}^{T}{\overset{\sim}{h}}_{5}} = {- {\overset{\sim}{R}}_{1,6}}}}}{{{\overset{\sim}{R}}_{2,6} = {{\frac{1}{{\overset{\sim}{R}}_{2,2}}{\overset{\sim}{h}}_{2}^{T}{\overset{\sim}{h}}_{6}} = {\overset{\sim}{R}}_{1,5}}};{{\overset{\sim}{R}}_{2,7} = {{\frac{1}{{\overset{\sim}{R}}_{2,2}}{\overset{\sim}{h}}_{2}^{T}{\overset{\sim}{h}}_{7}} = {- {\overset{\sim}{R}}_{1,8}}}};{{\overset{\sim}{R}}_{2,8} = {{\frac{1}{{\overset{\sim}{R}}_{2,2}}{\overset{\sim}{h}}_{2}^{T}{\overset{\sim}{h}}_{8}} = {\overset{\sim}{R}}_{1,7}}}}{{{\overset{\sim}{R}}_{3,3} = {{{\overset{\sim}{h}}_{3}} = {{\overset{\sim}{R}}_{1,1} = {\overset{\sim}{R}}_{2,2}}}};{{\overset{\sim}{R}}_{3,4} = {{\frac{1}{{\overset{\sim}{R}}_{3,3}}{\overset{\sim}{h}}_{3}^{T}{\overset{\sim}{h}}_{4}} = 0}};{{\overset{\sim}{R}}_{3,5} = {{\frac{1}{{\overset{\sim}{R}}_{3,3}}{\overset{\sim}{h}}_{3}^{T}{\overset{\sim}{h}}_{5}} = {{\overset{\sim}{R}}_{1,7} = {- {\overset{\sim}{R}}_{2,8}}}}}}{{{\overset{\sim}{R}}_{3,6} = {{\frac{1}{{\overset{\sim}{R}}_{3,3}}{\overset{\sim}{h}}_{3}^{T}{\overset{\sim}{h}}_{6}} = {{\overset{\sim}{R}}_{1,8} = {\overset{\sim}{R}}_{2,7}}}};{{\overset{\sim}{R}}_{3,7} = {{\frac{1}{{\overset{\sim}{R}}_{3,3}}{\overset{\sim}{h}}_{3}^{T}{\overset{\sim}{h}}_{7}} = {{\overset{\sim}{R}}_{1,5} = {\overset{\sim}{R}}_{2,6}}}}}{{\overset{\sim}{R}}_{3,8} = {{\frac{1}{{\overset{\sim}{R}}_{3,3}}{\overset{\sim}{h}}_{3}^{T}{\overset{\sim}{h}}_{8}} = {{- {\overset{\sim}{R}}_{1,6}} = {\overset{\sim}{R}}_{2,5}}}}{{{\overset{\sim}{R}}_{4,4} = {{{\overset{\sim}{h}}_{4}} = {{\overset{\sim}{R}}_{1,1} = {{\overset{\sim}{R}}_{2,2} = {\overset{\sim}{R}}_{3,3}}}}};{{\overset{\sim}{R}}_{4,5} = {{\frac{1}{{\overset{\sim}{R}}_{4,4}}{\overset{\sim}{h}}_{4}^{T}{\overset{\sim}{h}}_{5}} = {{- {\overset{\sim}{R}}_{1,8}} = {{\overset{\sim}{R}}_{2,7} = {- {\overset{\sim}{R}}_{3,6}}}}}}}{{{\overset{\sim}{R}}_{4,6} = {{\frac{1}{{\overset{\sim}{R}}_{4,4}}{\overset{\sim}{h}}_{4}^{T}{\overset{\sim}{h}}_{6}} = {{- {\overset{\sim}{R}}_{1,7}} = {{\overset{\sim}{R}}_{2,8} = {- {\overset{\sim}{R}}_{3,5}}}}}};{{\overset{\sim}{R}}_{4,7} = {{\frac{1}{{\overset{\sim}{R}}_{4,4}}{\overset{\sim}{h}}_{4}^{T}{\overset{\sim}{h}}_{7}} = {{\overset{\sim}{R}}_{1,6} = {{- {\overset{\sim}{R}}_{2,5}} = {- {\overset{\sim}{R}}_{3,8}}}}}}}{{\overset{\sim}{R}}_{4,8} = {{\frac{1}{{\overset{\sim}{R}}_{4,4}}{\overset{\sim}{h}}_{4}^{T}{\overset{\sim}{h}}_{8}} = {{\overset{\sim}{R}}_{1,5} = {{\overset{\sim}{R}}_{2,6} = {\overset{\sim}{R}}_{3,7}}}}}{{\overset{\sim}{R}}_{5,5} = {{{\overset{\sim}{h}}_{5}}^{2} - {\frac{1}{{\overset{\sim}{R}}_{1,1}^{2}}\begin{pmatrix}{\left( {{\overset{\sim}{h}}_{1}^{T}{\overset{\sim}{h}}_{5}} \right)^{2} - \left( {{\overset{\sim}{h}}_{2}^{T}{\overset{\sim}{h}}_{5}} \right)^{2} -} \\{\left( {{\overset{\sim}{h}}_{3}^{T}{\overset{\sim}{h}}_{5}} \right)^{2} - \left( {{\overset{\sim}{h}}_{4}^{T}{\overset{\sim}{h}}_{5}} \right)^{2}}\end{pmatrix}}}}{\overset{\sim}{R}}_{6,6} = {{{{\overset{\sim}{h}}_{6} - {\left( {{\overset{\sim}{q}}_{1}^{T}{\overset{\sim}{h}}_{6}} \right){\overset{\sim}{q}}_{1}} - {\left( {{\overset{\sim}{q}}_{2}^{T}{\overset{\sim}{h}}_{6}} \right){\overset{\sim}{q}}_{2}} - {\left( {{\overset{\sim}{q}}_{3}^{T}{\overset{\sim}{h}}_{6}} \right){\overset{\sim}{q}}_{3}} - {\left( {{\overset{\sim}{q}}_{4}^{T}{\overset{\sim}{h}}_{6}} \right){\overset{\sim}{q}}_{4}}}}^{2} = {{{\overset{\sim}{R}}_{5,5}{\overset{\sim}{R}}_{7,7}} = {{{{\overset{\sim}{h}}_{7} - {\left( {{\overset{\sim}{q}}_{1}^{T}{\overset{\sim}{h}}_{7}} \right){\overset{\sim}{q}}_{1}} - {\left( {{\overset{\sim}{q}}_{2}^{T}{\overset{\sim}{h}}_{7}} \right){\overset{\sim}{q}}_{2}} - {\left( {{\overset{\sim}{q}}_{3}^{T}{\overset{\sim}{h}}_{7}} \right){\overset{\sim}{q}}_{3}} - {\left( {{\overset{\sim}{q}}_{4}^{T}{\overset{\sim}{h}}_{7}} \right){\overset{\sim}{q}}_{4}}}}^{2} = {{\overset{\sim}{R}}_{5,5} = {{{\overset{\sim}{R}}_{6,6}{\overset{\sim}{R}}_{8,8}} = {{{{\overset{\sim}{h}}_{8} - {\left( {{\overset{\sim}{q}}_{1}^{T}{\overset{\sim}{h}}_{8}} \right){\overset{\sim}{q}}_{1}} - {\left( {{\overset{\sim}{q}}_{2}^{T}{\overset{\sim}{h}}_{8}} \right){\overset{\sim}{q}}_{2}} - {\left( {{\overset{\sim}{q}}_{3}^{T}{\overset{\sim}{h}}_{8}} \right){\overset{\sim}{q}}_{3}} - {\left( {{\overset{\sim}{q}}_{4}^{T}{\overset{\sim}{h}}_{8}} \right){\overset{\sim}{q}}_{4}}}}^{2} = {{\overset{\sim}{R}}_{5,5} = {{\overset{\sim}{R}}_{6,6} = {\overset{\sim}{R}}_{7,7}}}}}}}}}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack\end{matrix}$

Therefore, the matrix {tilde over (R)} of Equation 7 can be representedby using a closed-form formula as shown in Equation 9. Equation 8 andEquation 9, which are equations that are newly derived according to theexemplary embodiment of the present invention, can simply calculate thematrix {tilde over (R)} by reducing the number of matrix elements to becalculated.

$\begin{matrix}{\overset{\sim}{R} = \begin{bmatrix}{\overset{\sim}{R}}_{1,1} & 0 & 0 & 0 & {\overset{\sim}{R}}_{1,5} & {\overset{\sim}{R}}_{1,6} & {\overset{\sim}{R}}_{1,7} & {\overset{\sim}{R}}_{1,8} \\0 & {\overset{\sim}{R}}_{1,1} & 0 & 0 & {- {\overset{\sim}{R}}_{1,6}} & {\overset{\sim}{R}}_{1,5} & {- {\overset{\sim}{R}}_{1,8}} & {\overset{\sim}{R}}_{1,7} \\0 & 0 & {\overset{\sim}{R}}_{1,1} & 0 & {- {\overset{\sim}{R}}_{1,7}} & {\overset{\sim}{R}}_{1,8} & {\overset{\sim}{R}}_{1,5} & {- {\overset{\sim}{R}}_{1,6}} \\0 & 0 & 0 & {\overset{\sim}{R}}_{1,1} & {- {\overset{\sim}{R}}_{1,8}} & {- {\overset{\sim}{R}}_{1,7}} & {\overset{\sim}{R}}_{1,6} & {\overset{\sim}{R}}_{1,5} \\0 & 0 & 0 & 0 & {\overset{\sim}{R}}_{5,5} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {\overset{\sim}{R}}_{5,5} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {\overset{\sim}{R}}_{5,5} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & {\overset{\sim}{R}}_{5,5}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack\end{matrix}$

In addition, if {tilde over (q)}_(i), i=1, 2, . . . , 8, and denotes thei-th column of the matrix {tilde over (Q)}₁, her matrix {tilde over(Q)}₁ can be represented as shown in Equation 10 and each element of thematrix {tilde over (Q)}: can be represented as shown in Equation 11.

{tilde over (Q)} ₁ =:[{tilde over (q)} ₁ , {tilde over (q)} ₂ , {tildeover (q)} ₃ , {tilde over (q)} ₄ , {tilde over (q)} ₅ , {tilde over (q)}₆ , {tilde over (q)} ₇ , {tilde over (q)} ₈]  [Equation 10]

$\begin{matrix}{{{{{\overset{\sim}{q}}_{1} = {{\frac{1}{{\overset{\sim}{h}}_{1}}{\overset{\sim}{h}}_{1}} = {\frac{1}{{\overset{\sim}{R}}_{1,1}}{\overset{\sim}{h}}_{1}}}};{{\overset{\sim}{q}}_{2} = {\frac{1}{{\overset{\sim}{R}}_{2,2}}{\overset{\sim}{h}}_{2}}};{{\overset{\sim}{q}}_{3} = {\frac{1}{{\overset{\sim}{R}}_{3,3}}{\overset{\sim}{h}}_{3}}};{{\overset{\sim}{q}}_{4} = {\frac{1}{{\overset{\sim}{R}}_{4,4}}{\overset{\sim}{h}}_{4}}}}{\overset{\sim}{q}}_{5} = {\frac{1}{{\overset{\sim}{R}}_{5,5}}\left( {{\overset{\sim}{h}}_{5} - {{\overset{\sim}{R}}_{1,5}{\overset{\sim}{q}}_{1}} - {{\overset{\sim}{R}}_{2,5}{\overset{\sim}{q}}_{2}} - {{\overset{\sim}{R}}_{3,5}{\overset{\sim}{q}}_{3}} - {{\overset{\sim}{R}}_{4,5}{\overset{\sim}{q}}_{4}}} \right)}}{{\overset{\sim}{q}}_{6} = {\frac{1}{{\overset{\sim}{R}}_{6,6}}\left( {{\overset{\sim}{h}}_{6} - {{\overset{\sim}{R}}_{1,6}{\overset{\sim}{q}}_{1}} - {{\overset{\sim}{R}}_{2,6}{\overset{\sim}{q}}_{2}} - {{\overset{\sim}{R}}_{3,6}{\overset{\sim}{q}}_{3}} - {{\overset{\sim}{R}}_{4,6}{\overset{\sim}{q}}_{4}}} \right)}}{{\overset{\sim}{q}}_{7} = {\frac{1}{{\overset{\sim}{R}}_{7,7}}\left( {{\overset{\sim}{h}}_{7} - {{\overset{\sim}{R}}_{1,7}{\overset{\sim}{q}}_{1}} - {{\overset{\sim}{R}}_{2,7}{\overset{\sim}{q}}_{2}} - {{\overset{\sim}{R}}_{3,7}{\overset{\sim}{q}}_{3}} - {{\overset{\sim}{R}}_{4,7}{\overset{\sim}{q}}_{4}}} \right)}}{{\overset{\sim}{q}}_{8} = {\frac{1}{{\overset{\sim}{R}}_{8,8}}\left( {{\overset{\sim}{h}}_{8} - {{\overset{\sim}{R}}_{1,8}{\overset{\sim}{q}}_{1}} - {{\overset{\sim}{R}}_{2,8}{\overset{\sim}{q}}_{2}} - {{\overset{\sim}{R}}_{3,8}{\overset{\sim}{q}}_{3}} - {{\overset{\sim}{R}}_{4,8}{\overset{\sim}{q}}_{4}}} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack\end{matrix}$

When the matrixes {tilde over (Q)}₁ and {tilde over (R)} are calculatedin the above-described manner, the Equation 2 can be developed asEquation 12 by multiplying both sides of Equation 2 by {tilde over(Q)}₁.

{tilde over (Q)} ₁ ^(T) r={tilde over (Q)} ₁ ^(T) Hs+{tilde over (Q)} ₁^(T) n={tilde over (Q)} ₁ ^(T)({tilde over (Q)} ₁ {tilde over(R)})s+{tilde over (Q)} ₁ ^(T) n={tilde over (R)}s+{tilde over (Q)} ₁^(T) n   [Equation 12]

Equation 13 can be obtained by applying a minimum Euclidean detectionmethod to the above formula, and a Euclidean metric can be calculated asshown in Equation 14.

$\begin{matrix}{S^{sol} = {\arg \; {\min\limits_{S \in {(S_{M})}^{8}}{{{{\overset{\sim}{Q}}_{1}^{T}r} - {\overset{\sim}{R}s}}}^{2}}}} & \left\lbrack {{Equation}\mspace{14mu} 13} \right\rbrack \\{{{{{\overset{\sim}{Q}}_{1}^{T}r} - {\overset{\sim}{R}s}}}^{2} = {{{y - {\overset{\sim}{R}s}}}^{2} = {\left( {y_{8} - {{\overset{\sim}{R}}_{8,8}s_{8}}} \right)^{2} + \left( {y_{7} - {{\overset{\sim}{R}}_{7,7}s_{7}}} \right)^{2} + \left( {y_{6} - {{\overset{\sim}{R}}_{6,6}s_{6}}} \right)^{2} + \left( {y_{5} - {{\overset{\sim}{R}}_{5,5}s_{5}}} \right)^{2} + \begin{pmatrix}{y_{4} - {{\overset{\sim}{R}}_{4,4}s_{4}} - {{\overset{\sim}{R}}_{4,5}s_{5}} -} \\{{{\overset{\sim}{R}}_{4,6}s_{6}} - {{\overset{\sim}{R}}_{4,7}s_{7}} - {{\overset{\sim}{R}}_{4,8}s_{8}}}\end{pmatrix}^{2} + \begin{pmatrix}{y_{3} - {{\overset{\sim}{R}}_{3,3}s_{3}} - {{\overset{\sim}{R}}_{3,5}s_{5}} -} \\{{{\overset{\sim}{R}}_{3,6}s_{6}} - {{\overset{\sim}{R}}_{3,7}s_{7}} - {{\overset{\sim}{R}}_{3,8}s_{8}}}\end{pmatrix}^{2} + \begin{pmatrix}{y_{2} - {{\overset{\sim}{R}}_{2,2}s_{2}} - {{\overset{\sim}{R}}_{2,5}s_{5}} -} \\{{{\overset{\sim}{R}}_{2,6}s_{6}} - {{\overset{\sim}{R}}_{2,7}s_{7}} - {{\overset{\sim}{R}}_{2,8}s_{8}}}\end{pmatrix}^{2} + \begin{pmatrix}{y_{1} - {{\overset{\sim}{R}}_{1,1}s_{1}} - {{\overset{\sim}{R}}_{1,5}s_{5}} -} \\{{{\overset{\sim}{R}}_{1,6}s_{6}} - {{\overset{\sim}{R}}_{1,7}s_{7}} - {{\overset{\sim}{R}}_{1,8}s_{8}}}\end{pmatrix}^{2}}}} & \left\lbrack {{Equation}\mspace{14mu} 14} \right\rbrack\end{matrix}$

Here, y={tilde over (Q)}₁ ^(T)r and y_(i) denote the i-th element of y.

In addition, S_(M) denotes constellation and can be represented withM-ary pulse amplitude modulation (PAM) defined by Equation 15.

S _(M) :={−√{square root over (M)}+1,−√{square root over (M)}+3, . . . ,−1,1, . . . , √{square root over (M)}−3, [√{square root over(M)}−1}  Equation 15]

Conventionally, symbols (s_(i), i=1, . . . , 8) that minimize Equation14 (i.e., Euclidean metric) are simultaneously obtained, but accordingto the exemplary embodiment of the present invention, the thirdtransmission symbol and the last transmission symbol (i.e., x₃ and x₄)are detected first in order to reduce complexity. That is, real partsand imaginary parts (s_(i), i=5, . . . , 8) of the symbols x₃ and x₄that minimize the metric M₁ of Equation 16 are detected first.

M ₁=(y ₈ −{tilde over (R)} _(8,8) s ₈)²+(y ₇ −{tilde over (R)} _(7,7) s₇)²+(y ₆ −{tilde over (R)} _(6,6) s ₆)²+(y ₅ −{tilde over (R)} _(5,5) s₅)²   [Equation 16]

Here, the four terms are independent, and therefore the real parts andthe imaginary parts of the symbols x₃ and x₄ can be detected as shown inEquation 17.

s ^ k = S M  ( y k R k , k ) , k = 5 , 6 , 7 , 8 [ Equation   17 ]

Here,

S_(M)(•) denotes a projection function to the above-definedconstellation S_(M). That is, this function searches for the closestconstellation point among all constellation points of the constellationS_(M).

A real part and an imaginary part (s_(i), i=1, . . . , 4) of each of thetransmission symbols x₁ and x₂ are detected by using Equation 18. Thatis, the transmission symbols x₁ and x₂ that minimize the next metric M₂are detected.

$\begin{matrix}{M_{3} = {\begin{pmatrix}{y_{4} - {{\overset{\sim}{R}}_{4,4}s_{4}} - {{\overset{\sim}{R}}_{4,5}s_{5}} -} \\{{{\overset{\sim}{R}}_{4,6}s_{6}} - {{\overset{\sim}{R}}_{4,7}s_{7}} - {{\overset{\sim}{R}}_{4,8}s_{8}}}\end{pmatrix}^{2} + \begin{pmatrix}{y_{3} - {{\overset{\sim}{R}}_{3,3}s_{3}} - {{\overset{\sim}{R}}_{3,5}s_{5}} -} \\{{{\overset{\sim}{R}}_{3,6}s_{6}} - {{\overset{\sim}{R}}_{3,7}s_{7}} - {{\overset{\sim}{R}}_{3,8}s_{8}}}\end{pmatrix}^{2} + \begin{pmatrix}{y_{2} - {{\overset{\sim}{R}}_{2,2}s_{2}} - {{\overset{\sim}{R}}_{2,5}s_{5}} -} \\{{{\overset{\sim}{R}}_{2,6}s_{6}} - {{\overset{\sim}{R}}_{2,7}s_{7}} - {{\overset{\sim}{R}}_{2,8}s_{8}}}\end{pmatrix}^{2} + \begin{pmatrix}{y_{1} - {{\overset{\sim}{R}}_{1,1}s_{1}} - {{\overset{\sim}{R}}_{1,5}s_{5}} -} \\{{{\overset{\sim}{R}}_{1,6}s_{6}} - {{\overset{\sim}{R}}_{1,7}s_{7}} - {{\overset{\sim}{R}}_{1,8}s_{8}}}\end{pmatrix}^{2}}} & \left\lbrack {{Equation}\mspace{14mu} 18} \right\rbrack\end{matrix}$

A real part and an imaginary part (s_(i), i=1, . . . , 4) of each of thetransmission symbols x₁ and x₂ are calculated as shown in Equation 19.

s ^ k = S M  ( y k - R k , 5  s ^ 5 - R k , 6  s ^ 6 - R k , 7  s ^7 - R k , 8  s ^ 8 R k , k ) , k = 1 , 2 , 3 , 4 [ Equation   19 ]

FIG. 2 is a flowchart of a transmission symbol detection method at areceiving side according to the exemplary embodiment of the presentinvention.

Referring to FIG. 2, when a signal is received through a receivingantenna, a receiving side performs channel estimation by using thereceived signal in step S101, and generates an augmented channel matrix{tilde over (H)} that includes an estimated channel matrix H.

In Equation 2, the first two transmission symbols x₁ and x₂ (s₁, s₂, s₃,s₄) are received through channels h_(k,1) and h_(k,2) of thetransmitting antenna 1 and the transmitting antenna 2, and other twotransmission symbols x₃ and x₄ (s₅, s₆, s₇, s₈) are received throughchannels h_(k,3) and h_(k,4) of the transmitting antenna 3 and thetransmitting antenna 4.

Therefore, the first two transmission symbols x₁ and x₂ can be moreaccurately detected when the channels h_(k,1) and h_(k,2) of thetransmitting antennas 1 and 2 are in good condition, and the other twotransmission symbols x₃ and x₄ can be more accurately detected when thechannel h_(k,3) and h_(k,4) of the transmitting antennas 3 and 4 are ingood condition.

Accordingly, when transmission symbol detection is performed in theabove-described manner, the third and fourth transmission symbols x₃ andx₄ should be accurately detected for accurate detection of the first twotransmission symbols x₁ and x₂. When the channels h_(k,3) and h_(k,4) ofthe transmitting antennas 3 and 4 are in better condition than thechannels h_(k,1) and h_(k,2) of the transmitting antennas 1 andtransmitting antenna 2, the first two transmission symbols x₁ and x₂ aredetected first and then the other two transmission symbols symbol x₃ andx₄ are detected from better performance.

The receiving side checks channel condition of each transmissionantenna, and determines whether Equation 20 is satisfied (S102).

$\begin{matrix}{{\sum\limits_{k = 1}^{n_{r}}\; \left( {{h_{k,1}}^{2} + {h_{k,2}}^{2}} \right)} \leq {\sum\limits_{k = 1}^{n_{r}}\; \left( {{h_{k,3}}^{2} + {h_{k,4}}^{2}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 20} \right\rbrack\end{matrix}$

When Equation 20 is satisfied, the augmented channel matrix {tilde over(H)} is QR-decomposed on the basis of Equation 8 to 11 (S103), the thirdand fourth transmission symbols x₃ and x₄ are detected (S104), and thenthe first two transmission symbols symbol x₁ and x₂ are detected byusing the detected third and fourth transmission symbols x₃ and x₄(S105).

When Equation 20 is not satisfied in step 102, the channel matrix H anda transmission signal vector s are rearranged as shown in Equation 21 instep S106, and the QR decomposition is performed on the augmentedchannel matrix {tilde over (H)} that includes the rearranged channelmatrix H in step S107. The first two transmission symbols x₁ and x₂ aredetected first in step S108, and the other two transmission symbols x₃and x₄ are detected by using the two detected transmission symbols x₁and x₂ in step S109.

                                                            [Equation  21]$H = \begin{bmatrix}{\left\lbrack h_{1,3} \right\rbrack} & {- {\left\lbrack h_{1,3} \right\rbrack}} & {\left\lbrack h_{1,4} \right\rbrack} & {- {\left\lbrack h_{1,4} \right\rbrack}} & {\left\lbrack h_{1,1} \right\rbrack} & {- {\left\lbrack h_{1,1} \right\rbrack}} & {\left\lbrack h_{1,2} \right\rbrack} & {- {\left\lbrack h_{1,2} \right\rbrack}} \\{\left\lbrack h_{1,3} \right\rbrack} & {\left\lbrack h_{1,3} \right\rbrack} & {\left\lbrack h_{1,4} \right\rbrack} & {\left\lbrack h_{1,4} \right\rbrack} & {\left\lbrack h_{1,1} \right\rbrack} & {\left\lbrack h_{1,1} \right\rbrack} & {\left\lbrack h_{1,2} \right\rbrack} & {\left\lbrack h_{1,2} \right\rbrack} \\{\left\lbrack h_{1,4} \right\rbrack} & {\left\lbrack h_{1,4} \right\rbrack} & {- {\left\lbrack h_{1,3} \right\rbrack}} & {- {\left\lbrack h_{1,3} \right\rbrack}} & {\left\lbrack h_{1,2} \right\rbrack} & {\left\lbrack h_{1,2} \right\rbrack} & {- {\left\lbrack h_{1,1} \right\rbrack}} & {- {\left\lbrack h_{1,1} \right\rbrack}} \\{\left\lbrack h_{1,4} \right\rbrack} & {- {\left\lbrack h_{1,4} \right\rbrack}} & {- {\left\lbrack h_{1,3} \right\rbrack}} & {\left\lbrack h_{1,3} \right\rbrack} & {\left\lbrack h_{1,2} \right\rbrack} & {- {\left\lbrack h_{1,2} \right\rbrack}} & {- {\left\lbrack h_{1,1} \right\rbrack}} & {\left\lbrack h_{1,1} \right\rbrack} \\\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\{\left\lbrack h_{n_{r},3} \right\rbrack} & {- {\left\lbrack h_{n_{r},3} \right\rbrack}} & {\left\lbrack h_{n_{r},4} \right\rbrack} & {- {\left\lbrack h_{n_{r},4} \right\rbrack}} & {\left\lbrack h_{n_{r},1} \right\rbrack} & {- {\left\lbrack h_{n_{r},1} \right\rbrack}} & {\left\lbrack h_{n_{r},2} \right\rbrack} & {- {\left\lbrack h_{n_{r},2} \right\rbrack}} \\{\left\lbrack h_{n_{r},3} \right\rbrack} & {\left\lbrack h_{n_{r},3} \right\rbrack} & {\left\lbrack h_{n_{r},4} \right\rbrack} & {\left\lbrack h_{1,4} \right\rbrack} & {\left\lbrack h_{n_{r},1} \right\rbrack} & {\left\lbrack h_{n_{r},1} \right\rbrack} & {\left\lbrack h_{n_{r},2} \right\rbrack} & {\left\lbrack h_{n_{r},2} \right\rbrack} \\{\left\lbrack h_{n_{r},4} \right\rbrack} & {\left\lbrack h_{n_{r},4} \right\rbrack} & {- {\left\lbrack h_{n_{r},3} \right\rbrack}} & {- {\left\lbrack h_{1,3} \right\rbrack}} & {\left\lbrack h_{n_{r},2} \right\rbrack} & {\left\lbrack h_{n_{r},2} \right\rbrack} & {- {\left\lbrack h_{n_{r},1} \right\rbrack}} & {- {\left\lbrack h_{n_{r},1} \right\rbrack}} \\{\left\lbrack h_{n_{r},4} \right\rbrack} & {- {\left\lbrack h_{n_{r},4} \right\rbrack}} & {- {\left\lbrack h_{n_{r},3} \right\rbrack}} & {\left\lbrack h_{1,3} \right\rbrack} & {\left\lbrack h_{n_{r},2} \right\rbrack} & {- {\left\lbrack h_{n_{r},2} \right\rbrack}} & {- {\left\lbrack h_{n_{r},1} \right\rbrack}} & {\left\lbrack h_{n_{r},1} \right\rbrack}\end{bmatrix}$ $\begin{matrix}{s^{\prime}:=\left\lbrack {{\left\lbrack x_{3} \right\rbrack},{\left\lbrack x_{3} \right\rbrack},{\left\lbrack x_{4} \right\rbrack},{\left\lbrack x_{4} \right\rbrack},{\left\lbrack x_{1} \right\rbrack},{\left\lbrack x_{1} \right\rbrack},{\left\lbrack x_{2} \right\rbrack},{\left\lbrack x_{2} \right\rbrack}} \right\rbrack^{T}} \\{= {\text{:}\left\lbrack {s_{1}^{\prime},s_{2}^{\prime},s_{3}^{\prime},s_{4}^{\prime},s_{5}^{\prime},s_{6}^{\prime},s_{7}^{\prime},s_{8}^{\prime}} \right\rbrack}^{T}}\end{matrix}$

In Equation 21, a channel gain order included in the channel matrix Hand a location of a transmission symbol included in the transmissionsignal ( ) are reversed.

With reference to FIG. 3 to FIG. 5, an improved transmission symboldetection method will now be described in more detail.

FIG. 3 shows a typical SIC method in a case of using a binary phaseshift key (BPSK) method, and FIG. 4 shows an SIC method in a case ofusing a BPSK method according to the exemplary embodiment of the presentinvention. FIG. 5 shows a determination area for determining a feedbackdetection value when the SCI method is applied to 16-QAM according tothe exemplary embodiment of the present invention.

In the exemplary embodiment of the present invention, a successiveinterference cancellation (SIC) method is used for transmission symboldetection.

FIG. 3 shows a case of using a BPSK method as an exemplary use of theSIC method.

As shown in FIG. 3, when the SIC method is applied, the receiving sidedetects a transmission symbol by using a received signal, and thus thesymbol is determined to be 1 when the received signal s has a value thatis greater than 0. Otherwise, the symbol is determined to be −1. Thedetermination value ŝ is a detection value of the symbol s, and thissymbol detection value is used for the next symbol detection.

When using such an SIC method, previous accurate determination canresult in the next accurate determination. However, previous inaccuratedetermination has a bad influence on the next determination.Particularly, feeding back an inaccurate determination value to the nextdetermination is worse than feeding back nothing at all. For example,assume that the received signal value is +1 but the symbol is determinedto −1. In this assumption, the next determination performance may becomeworse when the inaccurate symbol value (i.e., −1) is fed back to thenext determination than when no value (i.e., 0) is fed back to the nextdetermination. In addition, the probability of detecting an inaccuratedetection value at the receiving side decreases as an absolute value ofthe received signal decreases.

Therefore, in order to improve performance of the SIC method, thedetermination area is changed as shown in FIG. 4 according to theexemplary embodiment of the present invention. Thus, when an absolutevalue of a received signal is smaller than a predetermined thresholdvalue in detection value determination, 0 rather than the detectionvalue is fed back. That is, the actual detection value is fed back onlywhen it is greater than the threshold value. In FIG. 4, δ denotes thethreshold value, ŝ denotes the actual detection value, and {tilde over(s)} denotes a value that is fed back to the next determination.

Although FIG. 3 and FIG. 4 show the case of using the BPSK modulationmethod, the present invention can be applied to M-QAM modulation, andFIG. 5 shows a determination area used for determining a detection valueto be fed back when the SIC method is applied to 16-QAM. As shown inFIG. 5, when a received signal exists inside dotted lines, the receivingside uses a value given as a solid line between two dotted lines as afeedback value instead of using an actually detected value.

As described, when detection values ({tilde over (s)}_(k),=1, 2, . . . ,8) are determined for all transmission symbols, all the detectionvalues, excluding {tilde over (s)}₈, are substituted to Equation 17 soas to detect the imaginary part s₈ of x₄ as shown in Equation 22.

s ^ 8 = S M  ( y 8  R ~ 8 , 8 + u 8 , 4  R ~ 4 , 8 + u 8 , 3  R ~ 3, 8 + u 8 , 2  R ~ 2 , 8 + u 8 , 1  R ~ 1 , 8 R ~ 8 , 8 2 + R ~ 4 , 82 + R ~ 3 , 8 2 + R ~ 2 , 8 2 + R ~ 1 , 8 2 )   u 8 , 4 = y 4 - R ~ 4, 4  s ~ 4 - R ~ 4 , 5  s ~ 5 - R ~ 4 , 6  s ~ 6 - R ~ 4 , 7  s ~ 7  u 8 , 3 = y 3 - R ~ 3 , 3  s ~ 3 - R ~ 3 , 5  s ~ 5 - R ~ 3 , 6 s ~ 6 - R ~ 3 , 7  s ~ 7   u 8 , 2 = y 2 - R ~ 2 , 2  s ~ 2 - R ~ 2, 5  s ~ 5 - R ~ 2 , 6  s ~ 6 - R ~ 2 , 7  s ~ 7   u 8 , 1 = y 1 -R ~ 1 , 1  s ~ 1 - R ~ 1 , 5  s ~ 5 - R ~ 1 , 6  s ~ 6 - R ~ 1 , 7 s ~ 7 [ Equation   22 ]

When the imaginary part s₈ of x₄ is detected, all the detection values,excluding {tilde over (s)}₇, are substituted to Equation 17 so as todetect the real part s₇ of x₄. In the same manner as above, the realpart and the imaginary part s₆ and s₅ of the candidate vector x₃ aredetected.

In addition, remaining transmission symbols are detected by usingEquation 23.

s ^ k = S M  ( y k - R k , 5  s ~ 5 - R k , 6  s ~ 6 - R k , 7  s ~7 - R k , 8  s ~ 8 R k , k ) , k = 1 , 2 , 3 , 4. [ Equation   23 ]

Until now, the transmission symbols have been detected by performing thedetection process once at the receiving side. However, according to theexemplary embodiment of the present invention, the above-describedtransmission symbol detection process is iteratively performed at thereceiving side so as to detect more accurate transmission symbols.

FIG. 6 shows an exemplary comparison result of a bit error rate (BER)between the transmission symbol detection method according to theexemplary embodiment of the present invention and typical ZF-SIC andMMSE-SIC methods. In this example, two receiving antennas and 4-QAM areused.

FIG. 6 shows that the transmission symbol detection method (i.e.,proposed method) according to the exemplary embodiment of the presentinvention results in performance that is much closer to the ML detectionmethod that the conventional detection methods (i.e., (ZF-SIC andMMSE-SIC). For example, in the BER of 10⁻³, performance of the proposedmethod is improved by 2 dB with zero iteration and 2.5 dB with oneiteration.

The following Table 1 compares the amount of calculation in the twocases with the assumption of using two transmitting antennas and QPSK.One case uses the transmission symbol detection method (proposed)according to the exemplary embodiment of the present invention, and theother case uses typical ZF-SIC and MMSE-SIC methods.

TABLE 1 Floating Floating point Floating Floating point Addition/ pointpoint Square Total Sub- Multipli- Divi- root CPU Method traction cationsion calculation cycles ZF-SIC 560 604 72 8 7492 MMSE-SIC 1072 1116 1368 13,892 Proposed(iter = 0) 144 154 20 2 1934 Proposed(iter = 1) 276 28640 6 3706

As shown in Table 1, the transmission symbol detection method accordingto the exemplary embodiment of the present invention requires much lesscalculation compared to the conventional methods (i.e., ZF-SIC andMMSE-SIC). For example, compared to the MMSE-SIC method, the proposedmethod requires an amount of CPU calculation of 14% with no iterationand requires an amount of CPU calculation of 27% with one iteration.That is, the proposed method according to the exemplary embodiment ofthe present invention can provide better performance with low complexitycompared to the existing detection methods.

The above-described embodiments can be realized through a program forrealizing functions corresponding to the configuration of theembodiments or a recording medium for recording the program in additionto through the above-described device and/or method, which is easilyrealized by a person skilled in the art.

While this invention has been described in connection with what ispresently considered to be practical exemplary embodiments, it is to beunderstood that the invention is not limited to the disclosedembodiments, but, on the contrary, is intended to cover variousmodifications and equivalent arrangements included within the spirit andscope of the appended claims.

1. A transmission symbol detection method of a multiple antenna systemincluding a plurality of transmission antennas, the transmission symboldetection method comprising: estimating a first matrix that is a channelmatrix including a plurality of channel gains respectively correspondingto the plurality of transmission antennas by using a received signal;calculating a second matrix that is an upper-triangle matrix and a thirdmatrix that is a unitary matrix from the first matrix; and detecting aplurality of transmission symbols by performing successive interferencecancellation (SIC) based on the second and third matrixes, wherein thesecond matrix comprises a first component that corresponds to a firstchannel gain of the first matrix and a second component that iscalculated based on the first channel gain and a second channel gainthat is different from the first channel gain as diagonal components,and further comprises a plurality of components by using the firstchannel gain and a plurality of channel gains that are different fromthe first channel gain.
 2. The transmission symbol detection method ofclaim 1, further comprising: checking channel condition of each of theplurality of transmission antennas; and determining a detection order ofthe plurality of transmission symbols based on the channel condition. 3.The transmission symbol detection method of claim 2, wherein theplurality of transmission symbols corresponds to a first symbol groupincluding a pair of first and second symbols and a second symbol groupincluding a pair of third and fourth symbols, and the determining of thedetection order detects the first symbol group first before the secondsymbol group when a channel condition of the first symbol group isbetter than that of the second symbol group.
 4. The transmission symboldetection method of claim 3, wherein the determining of the detectionorder further comprises rearranging the first matrix and a transmissionsignal based on the detection order.
 5. The transmission symboldetection method of claim 4, wherein the determining of the detectionorder comprises detecting the plurality of transmission symbols thatrepresent a minimum Euclidean metric by using the second and thirdmatrixes.
 6. The transmission symbol detection method of claim 5,wherein the detecting of the plurality of transmission symbolscomprises: detecting the first symbol group that minimizes a firstmetric; and detecting the second symbol group that minimizes a secondmetric.
 7. The transmission symbol detection method of claim 5, whereinthe detecting of the plurality of transmission symbols furthercomprises: detecting a plurality of detection values through successiveinterference cancellation; re-detecting the plurality of detectionvalues by using the plurality of detection values; and detecting theplurality of transmission symbols by iteratively performing there-detecting of the plurality of detection values.
 8. The transmissionsymbol detection method of claim 7, wherein the detecting of theplurality of detection values comprises: detecting a first detectionvalue that has at least one value among first, second, and third valuesbased on an absolute value of the received signal; and detecting asecond detection value by using the first detection value.
 9. Thetransmission symbol detection method of claim 7, wherein the detectingof the plurality of detection values comprises: checking a location ofthe received signal within a determination area that includes aplurality of areas respectively corresponding to the plurality ofdetection values and a plurality of boundaries respectively partitioningthe plurality of areas; determining a value that corresponds to alocation of a boundary as a detection value when the received signal isplaced within a predetermined area from the corresponding boundary; anddetermining a value of an area where the received signal is placedoutside the predetermined area from the corresponding boundary.
 10. Thetransmission symbol detection method of claim 1, wherein the second andthird matrixes are obtained by QR-decomposing the first matrix.